9.2 Systems of Linear Equations and Inequalities
Summative Worksheet #11: ANSWERS Check Homework PRE Objectives: To
solve systems using substitution.
Lesson 9.2 Systems of Linear Equations & Inequalities
Objectives: To solve systems using substitution. To solve systems
using elimination. To put systems into triangular form so they can
be solved with back substitution. For a system of linear equations
in twovariables, exactly one of the following is true.
The system has exactly one solution. The system has no solution.
The system has infinitely many solutions. Where the lines intersect
3 ways to kill a Vampire 1. Stake to the heart 2. Sunlight 3.
Garlic unless your Edward & a Cross 3 ways to solve Linear
Systems
1. By Graphing 2. By Substituting 3. Eliminating -1st make sure one
equation has a variable isolated
In this case, one already is: x = -2y + 2 -2nd Substitute the
expression into other equation Equation 1 x = -2y + 2 Equation 2 3
+ y = 16 -2y + 2 x -3rdSubstitute answer into one of the equations
3( )+ y = 16 -6y y = 16 3x = 16 (-2) y -5y + 6 = 16 x = 6 -5y = 10
y = -2 ( , ) x 6 -2 y -1st make sure one equation has a variable
isolated -2nd Substitute the expression into other equation
-3rdSubstitute answer into one of the equations + -y =3 3x += -9 3x
+ y = -9 -1y = 3 y = -3 -3 3x -3 = -9 3x = -6 (-2,-3) x = -2 - -6y
=-24 3x + 2y = 26 3x = 26 3x + 2y = 26 -6y =-24 ( ) y = 4 4 3x + 8
= 26 3x = 18 x = 6 (6, 4) Equation 1 3x 3y = 21 Equation 2 8x + 6y
= -14 -Multiply Equation 1 by 2 8x + 6y = -14 Equation 1 (2)3x
(2)3y = (2)21 6x 6y = 42 3x - 3y = 21 y = 21 + ( ) 14x + 0 =28 6 -
3y = 21 14x = 28 -3y = 15 x = 2 2 y = -5 (2, -5) Systems of Linear
Equations
Here are two examples of systems of linear equations in three
variables. System ofLinear Equations System inTriangular Form Ex 3.
Use back-substitution to solve the triangular system.
-Start with the last equation & solve upwards. Ex 4. Use
back-substitution to solve the triangular system.
-Start with the last equation & solve upwards. Classwork: Book:
pg. 657; 6-10 all Classwork: Book: pg. 649; 7-25 odd